What is expand [(k(k+1))/2 ]+(k+1) ?

The solution to expand [(k(k+1))/2 ]+(k+1) is (k^2)/2+k/2+k+1

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expand [(k(k+1))/2 ]+(k+1)

expand

[\frac{k ( k + 1 )}{2}] + (k + 1)

\frac{k ^{2}}{2} + \frac{k}{2} + k + 1

Solution steps

(\frac{k ( k + 1 )}{2}) + (k + 1)

Remove parentheses:

(a) = a

= \frac{k ( k + 1 )}{2} + k + 1

Expand

k (k + 1) : k^{2} + k

= \frac{k ^{2} + k}{2} + k + 1

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{k ^{2} + k}{2} = \frac{k ^{2}}{2} + \frac{k}{2}

= \frac{k ^{2}}{2} + \frac{k}{2} + k + 1

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16 cos^{4} (2 t) u (t - \frac{π}{4})

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(x^{2} + 2 x) ((2 x + 2) e^{x^{2} + 2 x})

What is expand [(k(k+1))/2 ]+(k+1) ?
The solution to expand [(k(k+1))/2 ]+(k+1) is (k^2)/2+k/2+k+1